Transformation of Strong Kernels
By definition, if K is a strong Carleman integral operator, then so is UKU* for every unitary operator U; also, Theorem 9.1 states that the class of bounded, strong Carleman integral operators is a two-sided ideal in the algebra of bounded operators. Actually, somewhat more can be said: if unbounded, strong Carleman integral operators exist, the class of not necessarily bounded, strong Carleman integral operators is closed under multiplication by arbitrary bounded operators from the right, or from the left.
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